$3\mathrm{.}3.$ The Commonwealth Banking Corporation issues a national credit card through its various

bank branches in five southeastern states. The bank credit card business is highly competitive

and interest rates do not vary substantially, so the company decided to attempt to retain its

customers by improving customer service through a reduction in billing errors. The credit card

division monitored its billing department process by taking daily samples of $200$ customer bills

for $30$ days and checking their accuracy. The sample results are as follows:

Develop a $p-$chart for the billing process using $3$ control limits and indicate if the process is

out of control.

$3\mathrm{.}28.$ The National Bank of Warwick is concerned with complaints from customers about its drive$-$through window operation. Customers complain that it sometimes takes too long to be served and since there are often cars in front and back of a customer, they cannot leave if the service is taking a long time. To correct this problem the bank installed an intercom system so the drive$-$through window teller can call for assistance if the line backs up or a customer has an unusually long transaction. The bank's objective is an average customer's waiting and service time of approximately three minutes. The bank's operations manager wants to monitor the new drive$-$through window system with SPC$.$ The manager has timed five customers' waiting and service times at random for $12$ days as follows:

$\backslash$table$[[,$Observation Times $($min$)],[$Sample$,1,2,3,4,5$

Factors for Determining Control Limits for $\stackrel{}{x}$ and $R-$Charts

$\backslash$table$[[\backslash$table$[[$Sample Size$],[n$

Problem $3-3($p$.141-11$th Ed$.)($The Commonwealth Banking...$)$

Problem $3-28($p$.146-11$th Ed$.)($The National Bank of Warwick...$)$

Note: Show Table with statistic$/$s $($i$.$e$.$ p$,$ x$-$bar, R$)$ calculated, draw control chart$/$s$,$ show all calculations, and mention comments $/$ observations for control charts $-$ like performed

in class. May solve using hand or use excel $($either is alright$).$